The advent of flat-panel televisions and mobile devices has accelerated the widespread use of small loudspeakers, which are well-known for their poor bass (i.e., low-frequency) performance. This characteristic typically places them in a disadvantageous position because a listener's overall impression of sound quality is strongly influenced by bass performance. It is, therefore, highly desirable to improve perceived bass performance, particularly with respect to devices that incorporate small loudspeakers.
A conventional approach to boosting bass performance is to simply amplify the low-frequency part of the audio spectrum, thereby making the bass sounds louder. However, the effectiveness of such an approach is significantly limited because small speakers typically have poor efficiency when converting electrical energy into acoustic energy at low frequencies, causing problems such as battery drain and overheating. A potentially even more serious problem is that amplification at low frequencies can cause excessive excursion of the loudspeaker's coil, leading to distortion and, in some cases, damage to the loudspeaker.
An alternative is to exploit the psychoacoustic effects of “virtual pitch”. For a simple example to illustrate this effect, consider a pitch with a fundamental frequency F0 of 100 Hertz (Hz). While the sensation of a 100 Hz pitch can by produced in the human ear by playing a pure tone of 100 Hz, musical instruments and human vocal cords usually produce this sensation using a set of tones with a complex harmonic structure, such as 100 Hz, 200 Hz, 300 Hz, etc., which can also provide a fuller (and differentiated) sound quality. What is more interesting is that the tone at the fundamental frequency of 100 Hz is not necessary for people to have the sensation of hearing a 100 Hz pitch. Even if the tone of 100 Hz is missing, a set of harmonic tones at 200 Hz, 300 Hz, 400 Hz, etc., can still produce the sensation of a 100 Hz pitch. The human ear apparently can infer the pitch from the harmonic tones alone. This phenomenon is referred to as virtual pitch.
One ramification of the concept of virtual pitch is that we do not need to physically produce a tone at the fundamental frequency F0 in order to produce the sensation of a pitch at F0. When applied to bass enhancement of small loudspeakers, this means that we do not need to waste energy at low frequencies where small loudspeakers are not efficient. Instead, we can produce a similar bass impression by using higher frequency tones, which a loudspeaker is more efficient at producing. As long as an appropriate harmonic structure is provided, the virtual pitch effect can be strong enough to produce a strong bass sensation. This general approach is referred to herein as virtual bass.
Early virtual bass techniques work in the time domain and generally involve the following steps:                1. Extract low-frequency components from the input audio signal using a bandpass filter to form a bass signal;        2. Generate higher-order harmonics by feeding the bass signal through a nonlinear device;        3. Select a portion of the high-order harmonics (virtual pitch) using a bandpass filter; and        4. Add the selected high-order harmonics back into the original signal.However, the present inventor has recognized that there are problems with this approach, including the introduction of intermodulation distortion by the nonlinear device, which can significantly degrade audio quality.        
More recent techniques work in the frequency domain using phase vocoders, e.g., as follows:                1. Use a short time Fourier transform (STFT) to transform the input audio signal into the discrete Fourier transform (DFT) domain;        2. Linearly scale up the frequencies of the low-frequency harmonic tones to frequencies at which the loudspeaker can efficiently produce sound;        3. Use the scaled-up harmonic frequencies to drive sum-of-sinusoids synthesizers to synthesize a time-domain virtual bass signal; and        4. Add the virtual bass signal back into the original signal.However, the present inventor has recognized at least one problem with this approach—that it causes the frequency differences between the harmonic tones also to be scaled up, so the resulting virtual pitch frequency is higher than it should be. In other words, the resulting virtual bass typically will be perceived as having a higher pitch than the bass portion of the original signal. Even worse, in many cases, particularly where music is involved, the foregoing shift in perceived pitch will then cause the perceived bass to clash with the other portions of the audio signal, resulting in an even more severe degradation of the sound quality.        